Let us comment in more detail how this relates to the gravitational gluing construction used in Ref. [1]}.
There, the canonical purification \(\mathinner {|{\sqrt{\rho _{AB}}}\rangle }_{A A^\star B B^\star }\)  was described as dual to a particular bulk geometry, the one formed by gluing two copies of the \(AB\)  entanglement wedge together.
If we naively follow this procedure for a random tensor network we arrive at the following picture. Firstly the entanglement spectrum of \(\rho _{AB}\)  is flat in this case, so up to normalization we can replace \(\rho _{AB}^{1/2}\)  by \(\rho _{AB}\) . Then seemingly the gluing procedure automatically follows, since we know there is an isometry from the bulk legs at the \(AB\)  RT surface to the \(AB\)  boundary legs and \(\rho _{AB}\)  already contains two copies of the tensor network for the bra and the ket [2]}.
